Thermopower mapping of superconducting cuprates

ABSTRACT

The invention comprises a method for determining the hole or electron concentration, transition temperature, ratio T c  /T c  (max), or state of doping of a material capable of exhibiting superconductivity when cooled below its critical temperature, by measuring the thermopower of a sample of the material above the critical temperature of the material and determining from the thermopower the hole or electron concentration, transition temperature, ratio T c  /T c  (max), or state of doping of the material as to whether it is underdoped, overdoped or optimally doped. The sample may be differentially heated and/or cooled to generate a temperature difference across the sample, the temperature difference across the sample measured, the voltage across the sample measured, and the hole concentration or similar determined from the measured temperature difference and the measured voltage. Means for determining the hole concentration, transition temperature, or doping of the material is also claimed.

TECHNICAL FIELD

The present invention comprises a method and means for determining thedoped or chemical hole concentration in high-T_(c) superconductingcuprates and related compounds.

The high-T_(c) superconducting cuprates all have in common square-planarsheets of CuO₂ with Cu occupying the B-site of a perovskite unit and Oatoms in the perovskite anion sites linking the corner-shared Cu atoms.These CuO₂ planes are the essential structural ingredient forsuperconductivity in these cuprate perovskites and superconductivityarises when holes or electrons are doped into the planes to aconcentration exceeding a minimum (p_(min) for holes, n_(min) forelectrons) and less than a maximum (p_(max) and n_(max) respectively).Without loss of generality, the bounds are established as p_(min) ≈0.05holes/Cu and p_(max) ≈0.27 holes/Cu for the hole-type superconductors(see Presland et al, Physica C 176 (1991) 95-105), but are not yetclearly determined for the electron superconductors. In thisspecification the invention is described with reference to thehole-superconductors but qualitatively similar, although numericallydifferent bounds are believed to apply for the electron superconductorsand the invention and general principles disclosed herein also haveapplication to the electron superconductors as will be apparent.

FIG. 1 shows this general superconducting phase behaviour for thehole-doped superconductors. Superconductivity occurs for about0.05≦p≦0.27 and T_(c) rises to a maximum T_(c) (max) at p˜0.16 followingan approximately parabolic dependence on p, conveniently and withoutloss of generality, given by

    T.sub.c /T.sub.c (max)≈1-82.6(p-0.16).sup.2        ( 1)

For about p<0.05 the behaviour is semiconducting and insulating as T→0while for about p>0.27 normal metallic behaviour occurs. The paraboliccurve in FIG. 1 was fitted to the data reported by Torrance et al, Phys.Rev. B40 (1989) 8872 and Takagi et al, Phys. Rev. B40 (1989) 2254, butit is likely that all other superconducting cuprates follow a similarcurve. The domain p<0.16 is referred to as underdoped and p>0.16 asoverdoped. Because of this common phase behaviour which is general tothe superconducting cuprates, the chemical hole concentration is animportant parameter whose determination makes it possible to locate acompound on the superconducting phase diagram, and moreover indicateswhether, and by how much, the doping need be altered to maximise T_(c)at T_(c) (max). Alternatively doping may be altered to maximise thecritical current of the superconductor. To maximise critical current thematerial is generally overdoped to a degree. This doping can becontrolled by alter-valent cation substitution or by changing the oxygencontent in the cuprate. Such chemical manipulation is preferably carriedout in such a way as to maintain the integrity of the CuO₂ planes andminimise disorder on these planes which can diminish T_(c), by pairbreaking, below the ideal phase curve T_(c) =T_(c) (p). Measurement andcontrol of the value of p allows the superconducting state to befine-tuned.

BACKGROUND ART

Standard measurement of p is by determination of the cation compositionby chemical analysis and determination of the oxygen content by hightemperature thermal gravimetry during reduction in hydrogen or bychemical titration. These methods are complex, slow and destructive tothe sample and with many of the superconducting cuprates is ambiguousbecause of mixed valency in solution.

DISCLOSURE OF INVENTION

In broad terms the invention comprises a method for determining the holeor electron concentration, transition temperature, ratio T_(c) /T_(c)(max), or the state of doping of a material capable of exhibitingsuperconductivity when cooled below its critical temperature, comprisingmeasuring the thermopower of a sample of the material above the criticaltemperature of the material and determining from the thermopower thehole or electron concentration, transition temperature, ratio T_(c)/T_(c) (max), or whether the material is underdoped, overdoped oroptimally doped for maximum T_(c) or critical current.

The method of the invention may include subjecting the sample to heatingand/or cooling to generate a temperature difference across the sample,measuring the temperature difference across the sample, measuring theelectrical potential difference or voltage across the sample, anddetermining from the measured temperature difference and the measuredelectrical potential difference or voltage across the sample the hole orelectron concentration, transition temperature, ratio T_(c) /T_(c)(max), or state of doping of the material.

The invention also comprises means for determining the hole or electronconcentration, transition temperature, ratio T_(c) /T_(c) (max), orstate of doping of a material capable of exhibiting superconductivitybelow its critical temperature, comprising:

two electrodes to contact a sample of the material between theelectrodes,

means for heating and/or cooling one or both of the electrodes togenerate a temperature difference between the electrodes,

temperature sensing means to indicate the temperature difference betweenthe electrodes,

means to measure the electrical potential difference or voltage betweenthe electrodes, and

means to determine from the measured temperature difference and themeasured electrical potential difference or voltage between theelectrodes the hole or electron concentration, transition temperature,ratio T_(c) /T_(c) (max) or state of doping of the material.

With the method of the invention the thermopower of a sample is measuredat a given temperature, which may be room temperature, and the hole orelectron concentration is determined from the measured thermopower. Themethod of the invention is simple, direct and non-destructive fordetermining p, and provides significant advantage in characterisingthese cuprates and assessing whether a superconducting cuprate is atoptimum doping level. The process can be carried out quickly and isreliable and non-destructive.

By "superconducting cuprate" it is intended to mean theperovskite-related superconductors containing Cu and 0 atoms typicallyin square-planer CuO₂ sheets. These superconductors are commonlyreferred to as high-T_(c) superconductors or high-temperaturesuperconductors even though transition temperatures in some may be lowerthan 15K, for example, Bi₂ Sr₂ CuO₆. In some of these compounds theremay be oxygen deficiency or excess in the CuO₂ sheets. Thesuperconducting cuprates include without loss of generality RBa₂ Cu₃O₇₋δ, RBa₂ Cu₄ O₈, R₂ Ba₄ Cu₇ O₁₅₋δ where R may be Y or a lanthaniderare-earth element, Bi₂ Sr₂ Ca_(n-1) Cu_(n) O_(2n+4), Tl_(m) Ba₂Ca_(n-1) Cu_(n) O_(2n+m+2) where n=1, 2, 3 or 4 and m=1 or 2, La_(2x)Sr_(x) CuO₄, Tl₀.5 Pb₀.5 Sr₂ Ca_(n-1) Cu_(n) O_(2n+3) where n=1, 2, 3 or4 and many other such-like compounds which are well-known to thoseskilled in the art. These superconducting materials also include themany cation-substituted derivative compounds also well-known to thoseskilled in the art. The superconductors may be in bulk sintered ormelt-processed form, thin films, thick films, wires or any compositeform with metals or ceramics for substrates or sheathing.

BRIEF DESCRIPTION OF THE DRAWINGS

In the figures shown:

FIG. 1 is the schematic normalised plot of the superconducting phasediagram for cuprates as a function of the doped hole concentration.

FIG. 2 is a schematic plot of the temperature dependence of thethermopower for superconducting cuprates for a range of holeconcentrations across the superconducting phase diagram. The light solidcurves are for the non-superconducting compositions while the heavysolid curves are for superconducting compositions. The dashed extensionsshow the expected thermopower in the absence of superconductivity andthe vertical arrow shows the fluctuation contribution.

FIG. 3 shows the temperature dependence of the thermopower for threecompositions with p˜p_(min) (2212-Bi, 123 and 1212-Tl), three withp˜p(T_(c) =T_(c) (max)) (2212-Bi, 1212-Tl and 2223-Tl), and one forp˜p_(max) (2201-Tl).

FIG. 4 shows the room temperature thermopower S(290K) plotted as afunction of the hole concentration, p for a variety of superconductingcuprates.

FIG. 5 shows the temperature dependence of the thermopower for Tl-2223(A) as synthesised (T_(c) ˜118K) and (B) after vacuum annealing (T_(c)˜128K).

FIG. 6 shows the temperature dependence of the thermopower for Bi-2223as synthesised (triangles) and after loading oxygen by annealing inoxygen at 370° C. (diamonds) and 300° C. (crosses).

FIG. 7 shows the room temperature thermopower S(290K) plotted as afunction of hole concentration for a variety of superconducting cupratesas in FIG. 4 but YBa₂ Cu₃ O₇₋δ has been quenched to preventoxygen-vacancy ordering.

FIG. 8 shows a schematic diagram of a device for measuring thethermopower quickly and easily.

FIG. 9 shows transition temperature T_(c) plotted against the roomtemperature thermopower S(290) for Yb₀.7 Ca₀.3 Ba₁.6 Sr₀.4 Cu₃ O₇₋δ forseveral different oxygen contents, δ.

FIG. 10 shows S(290) plotted against the hole concentration for Yb₀.7Ca₁₀.3 Ba₁.6 Sr₀.4 Cu₃ O₇₋δ deduced using equation (1).

DETAILED DESCRIPTION

FIG. 2 shows a schematic diagram of the temperature dependence of thethermopower for model cuprates at different hole concentrations, p, i.e.at different points across the phase curve. In the semiconducting domainthe thermopower rises with increasing temperature to a peak which islarge in value (100-500 μV/K) but in the superconducting compositions asp increases through 0.16, the peak moves to lower temperatures and abovethe peak the thermopower is linear in temperature. For larger values ofp the linear behaviour is simply displaced downwards with little changein slope. At the hole concentration corresponding to T_(c) (max) thethermopower at room temperature S(290K) is only slightly positive (2 to3 μV/K) and changes sign in the overdoped region at a value of pslightly larger than that corresponding to T_(c) (max). With continueddoping, T_(c) falls again and the linear T-dependent thermopower isdisplaced further downwards until, at p˜p_(max) where T_(c) falls tozero, the thermopower is negative for all T and linear through theorigin, i.e. it shows ideal metallic behaviour for a narrow bandwidthmetal. Actual T-dependent data is shown in FIG. 3 for YBa₂ Cu₃ O₇₋δ(123), Bi₂ Sr₂ CaCu₂ O₈ (2212), Tl₀.5 Pb₀.5 Sr₂ CaCu₂ O₇ (Tl-1212), Tl₂Ba₂ Ca₂ Cu₃ O₁₀ (Tl-2223) and Tl₂ Ba₂ CuO₆ (Tl-2201). 123, Bi-2212(single-crystal) and Tl-1212 are shown at p=p_(min), the latter two withY substituted for Ca to reduce p; Bi-2212, Tl-1212 and Tl-2223 are shownat T_(c) =T_(c) (max) and Tl-2201 is shown at p=p_(max) --the onlycompound for which data is available at this value of p. Thesingle-crystal data for Bi-2212 is the a-b plane thermopower which inceramic samples dominates over c-axis thermopower. The striking resultillustrated by this figure is that for all of these varied compounds thethermopower has the same magnitude and T-dependence for a given value ofp or for a given location on the superconducting phase curve,irrespective of whether the material is a sintered ceramic or a singlecrystal. It should be noted that for the optimum value of p for whichT_(c) =T_(c) (max) the thermopower S(T) rises to a maximum of 6 to 7μV/K, then falls linearly to S(290)˜2 to 3 μV/K at room temperature. Thethermopower appears to be unaffected by granularity and porosity. Thedata in FIG. 3 shows that a single-band model is applicable for thethermopower and there is no significant contribution from thecharge-reservoir layers, Bi₂ O₂, Tl₂ O₂ and (Tl, Pb)O. The chain layerin 123 does contribute a component to the temperature-dependentthermopower which has positive slope when fully oxygen loaded (δ˜0.0)but when oxygen deficient (δ>0) the chains do not contributesignificantly. This figure also implies that the thermopower has asimple universal dependence on p. This is quantified--in FIG. 4 wherethe room temperature thermopower, S(290) is plotted as a function of pfor all of the cuprates investigated. The values of p are determinedeither from bond valence sums using the parameter V₋₋ =2+V_(cu) -V₀₂-V₀₃ (Tallon, Physica C 176 (1991) 547-550) or from the relative valuesof T_(c) and T_(c) (max) using equation (1). The data is plotted on alogarithmic scale in the underdoped region and on a linear scale in theoverdoped region. Evidently the data for all of the compoundsinvestigated fall on a single curve. Notably, S(290) on the universalcurve changes sign just beyond p˜0.16, i.e. just beyond T_(c) (max). Bymeasurement of room temperature thermopower in any of these cuprates adirect deduction of the chemical hole concentration can be made byreferring to this universal curve shown in FIG. 4 or a similar curve orinformation reflecting such a curve. Such a measurement is simple, quickand non-destructive.

FIG. 8 shows a device (used in the following examples) for use with themethod of the invention. The device was constructed using copper, andinsulating components. This comprises a spring-loaded sample holder withheater (1) in the form of an electrical coil on the shaft of a fixedcopper anvil (2) forming one electrode and a diode thermometer (3) on asecond copper anvil (4) forming a second electrode, which is thrustagainst the sample by a spring (5) which is held by the locator post(6). The second, moveable anvil and spring can be relocated using thelocator screw (7) which slides in a slot (8). In this way samples ofwidely varying geometry and size can be mounted in the device. The facesof the two anvils forming the electrodes have recessed copper-constantinthermocouples connected in differential fashion to determine thetemperature difference between the two anvils and the two anvils havecopper wires attached to allow measurement of the voltage differencebetween them. Microvoltmeters are used to measure the thermocouplevoltage and the thermo-electric voltage induced between the electrodeswhen in operation. The device may be mounted on a long thin-walledstainless-steel tube with the electrical wires fed through the bore ofthe tube to allow dipping the device in a liquid helium dewar. In thisway the thermoelectric power S(T) can be determined from roomtemperature down to 4K.

A measuring instrument of the invention may comprise two electrodes,with one arranged to be heated (or one cooled or one heated and theother cooled), a temperature sensing means for indicating thetemperature difference between the two electrodes, and thermocouples asin the FIG. 8 device or other means for indicating the potentialdifference between the two electrodes, and a microprocessor controllerincluding a look-up table of data reflecting the universal curve of FIG.4 or a similar curve to provide a readout of hole concentration for anysamples measured (or electron concentration or the software could beconfigured to provide a readout of transition temperature, the ratioT_(c) /T_(c) (max) or a readout indicating whether the sample isunderdoped, overdoped or at optimal doping to maximise T_(c)).

The method of the invention is further illustrated by the followingexamples:

EXAMPLE 1

The record T_(c) value for any superconductor is exhibited by theTl-2223 compound. This compound may have Ca occupying a fraction of theTl sites and the chemical formula is more nearly Tl₁.7 Ba₂ Ca₂.3 Cu₃O₁₀₊δ. As synthesised in oxygen at 1 atmosphere pressure T_(c) ˜118K. Asingle-phase pellet of 2223 was prepared in the usual manner, thensubjected to up to 10 days annealing, sealed under vacuum in a quartztube. T_(c), as measured from DC magnetisation, was raised to 128K. Thisis the highest reproducible T_(c) exhibited by any superconductor. T_(c)was raised in this case by a hole-doping process, possibly migration ofCa onto Tl-sites, or possible Tl loss by evaporation. The questionremains as to whether T_(c) can be further raised by further holedoping, for example, by loading additional oxygen or by further vacuumannealing. FIG. 5 shows the measured thermopower for the sample before(T_(c) ˜118K) and after (T_(c) ˜128K) vacuum annealing. In the formercase the thermopower is typical of an underdoped sample, but in thelatter it is typical of an optimally doped cuprate superconductor withT_(c) =T_(c) (max). S(T) rises to a maximum of ˜8 μV/K then fallslinearly by -3 μV/K at room temperature. On this basis, because T_(c)varies only weakly with p near the peak in the parabola, it cannot beexpected to be raised more than another 1K. Indeed, subsequent oxygenloading, i.e. further hole doping, resulted in T_(c) falling by about1K. T_(c) (max) would appear to be close to 128K for this compound. Thisresult would have been ascertained just from measuring the roomtemperature value of the thermopower.

EXAMPLE 2

A sample of (Bi,Pb)₂ Sr₂ Ca₂ Cu₃ O₁₀ was synthesised by conventionalsolid state reaction. As-synthesised T_(c) =104K and the temperaturedependence of the thermopower was measured. This is shown in FIG. 6 bythe triangles. The maximum value of the thermopower S(max)˜12.5 μV/Kwhile the room temperature value S(290)˜6 μV/K. It is clear from thesevalues by consulting FIGS. 3 and 4, that the compound is slightlyunderdoped relative to T_(c) (max). The sample was annealed in flowingoxygen at 370° C. for 12 hours and then at 300° C. for 12 hours. Aftereach anneal, the temperature dependence of the thermopower was measuredas shown by the diamonds and crosses in FIG. 6. By comparing with FIGS.3 and 4 it is now clear that this sample is optimally doped for T_(c)=T_(c) (max) and indeed T_(c) had risen to 107K.

EXAMPLE 3

The only exception to the common behaviour shown in FIG. 4 is thethermopower data for YBa₂ Cu₃ O₇₋δ where near S=70 μV/K the data fallsbelow that for other cuprate superconductors. This may arise fromcontributions to the thermopower from the CuO chains in the structure.When δ lies between 0.4 and 0.6 the oxygen vacancies have a tendency toorder so that the chains alternate between full oxygen occupancy andfull oxygen vacancy. The chains thus alternate with the composition . .. --Cu--CuO--Cu--CuO-- . . . . Every second chain which is fullyoxygenated has a high electrical conductivity compared to the CuO₂planes for this region and since the contributions to the totalthermopower from the chain and plane subsystems are weighted by theirrespective electrical conductivities then there is a significantcontribution arising from the chains. The chain-originating thermopoweris low (<10 μV/K) and consequently the total thermopower falls belowthat for other superconducting cuprates which do not possess chainsubsystems. YBa₂ Cu₃ O₇₋δ was annealed and quenched rapidly into liquidnitrogen sufficient to ensure that oxygen vacancy ordering could nottake place. The disorder thus induced and frozen in on the chainsensures that the thermopower is not significantly affected by thechains. The data thus obtained is shown in FIG. 7 and evidently the YBa₂C₃ O₇₋δ data now matches that of the other superconducting cuprates.

EXAMPLE 4

A sample of Yb₀.7 Ca₀.3 Ba₁.6 Sr₀.4 Cu₃ O₇₋δ was prepared by synthesisat 850° C. in flowing gas of 1% oxygen and 99% nitrogen. The sample wasloaded with oxygen by slow cooling to 380° C. in oxygen at 40 barpressure. The sample, in the form of a 12 mm diameter pelletapproximately 2 mm thick, was placed and clamped between thespring-loaded anvils of the device of FIG. 8 and the thermoelectricpower measured at room temperature. The whole operation of mounting andmeasurement takes no more than 100 seconds including applying the heatercurrent and waiting for equilibration. The sample was then annealed in acertain oxygen partial pressure and temperature and after equilibrationwas quenched out into liquid-nitrogen in order to freeze in the newoxygen content (as quantified by 6 in the chemical formula). The roomtemperature thermoelectric power was remeasured in the device and thisprocess repeated for a variety of values of δ. Superconductingtransition temperatures were also measured for each of these annealedsamples. FIG. 9 shows T_(c) plotted against the room temperaturethermopower (S(290K)). T_(c) is seen to be maximised for S(290)˜2 μV/Kexactly as proposed from FIGS. 4 or 7. The hole concentration, p, isestimated from T_(c) /T_(c) (max) using equation (1) and S(290) isplotted against p in FIG. 10. Comparison with FIG. 4 or 7 shows that thebehaviour of the sample follows the universal curve in precisequantitative fashion.

The scope of the invention is defined in the following claims:

What is claimed is:
 1. A method for determining the hole or electronconcentration, transition temperature, ratio T_(c) /T_(c) (max), orstate of doping of a material capable of exhibiting superconductivitywhen cooled below its critical temperature, comprising measuring thethermopower of a sample of the material at a temperature above thecritical temperature of the material and determining from thethermopower the hole or electron concentration, transition temperature,ratio T_(c) /T_(c) (max), or state of doping of the material as towhether it is underdoped, overdoped or optimally doped for maximum T_(c)or critical current.
 2. A method of determining the hole or electronconcentration, transition temperature, ratio T_(c) /T_(c) (max), orstate of doping of a material capable of exhibiting superconductivitybelow its critical temperature, comprising subjecting the sample toheating and/or cooling to generate a temperature difference across thesample, measuring the temperature difference across the sample,measuring the electrical potential difference or voltage across thesample, and determining from the measured temperature difference and themeasured electrical potential difference or voltage across the samplethe hole or electron concentration, transition temperature, ratio T_(c)/T_(c) (max), or state of doping of the material as to whether it isunderdoped, overdoped or optimally doped for maximum T_(c) or criticalcurrent.
 3. A method according to claim 2 comprising holding the sampleof material between two electrodes and heating and/or cooling one orboth of the electrodes to generate the temperature difference betweenthe electrodes, measuring the temperature difference across the materialby measuring the temperature difference between the electrodes, andmeasuring the electrical potential difference or voltage across thematerial by measuring the electrical potential difference or voltagebetween the electrodes.
 4. A method according to any one of claims 1 to3, wherein the superconductor is a cuprate-based superconductorincluding a high T_(c) superconductor.
 5. A method as claimed in any oneof claims 1 to 3 wherein the superconductor is a hole-doped cupratesuperconductor.
 6. A method according to claim 4 wherein thesuperconductor comprises:a) RBa₂ Cu₃ O₇₋δ, RBa₂ Cu₄ O₈, or R₂ Ba₄ Cu₇O₁₅₋δ where R is Y or a lanthanide rare-earth element, or a derivativethereof obtained by partial substitution of Ba or Cu; b) Bi₂ Sr₂Ca_(n-1) Cu_(n) O_(2n+4) where n=1, 2, 3 or 4, or a derivative thereofobtained by partial substitution of Bi, Sr, Ca or Cu; c) Tl_(m) Ba₂Ca_(n-1) Cu_(n) O_(2n+m+2) where n equals 1, 2, 3 or 4 and m equals 1 or2 or a derivative thereof obtained by partial substitution of Tl, Ba, Caor Cu; d) La_(2x) Sr_(x) CuO₄ where x is between 0 and 0.35 or aderivative thereof obtained by partial substitution of La, Sr or Cu; ande) Tl₀.5 Pb₀.5 Sr₂ Ca_(n-1) Cu_(n) O_(2n+3) where n equals 1, 2, 3 or 4or a derivative thereof obtained by partial substitution of Tl, Pb, Sr,Ca and Cu.
 7. Means for determining the hole or electron concentration,transition temperature, ratio T_(c) /T_(c) (max), or doping of amaterial capable of exhibiting superconductivity below its criticaltemperature, comprising:two electrodes to contact a sample of thematerial between the electrodes, means for heating and/or cooling one orboth of the electrodes to generate a temperature difference between theelectrodes, temperature sensing means to indicate the temperaturedifference between the electrodes, means to measure the electricalpotential difference or voltage between the electrodes, and means todetermine from the measured temperature difference and the measuredelectrical potential difference or voltage between the electrodes thehole or electron concentration, transition temperature, ratio T_(c)/T_(c) (max) or state of doping of the material for maximum T_(c) orcritical current.